Awesome Music: Just about the entire soundtrack, which was composed by Akira Miyagawa, the son of Hiroshi Miyagawa, who did the soundtrack for the original series.
First explicit mention goes naturally to the opening. Having Isao Sasaki sing it is just icing on the cake of awesome. The second ending is also awesome in a nostalgic way, the perfect song for a space romance.
Also, "The Galactic Pilot". This is the song the crew of the Yukikaze sings as they go for their final battle, and its background music version plays as the fleet leave's for Plan M.
The Gamilas Empire's anthem is a stirring military-sounding march that sounds awesome whether it's the crews of the Yamato and a number of Gamilans singing it together, or the Gamilans bombing a planet to atoms.
Crazy Awesome: Some of what the Yamato pulled falls under this, like breaking through Deslar's trap of a star before them, an all-devouring thing and a warship before them and nowhere else to go by opening a path in the star's corona with the Wave Motion Gun and letting the star destroy the chasers, or breaking through Domel's ambush (actually only the first layer, as he had ships in reserve converge on the position just in case) by ramming Domel's flagship and moving her out of the course after blasting her at point blank. Domel's own face after the latter showed he too was thinking this. Let's also not forget the time Yamato charged through half of the entire Gamilan fleet to get to a warp gate after hiding inside Balun to fake being destroyed, then turned around and fired its Wave Motion Gun at Balun, destroying it and nearly all of the ships there, and stranding all the surviving ships in that sector of space since they can't use the warp gates anymore.
Hilarious in Hindsight: Voice-acting wise, Dessler's VA voiced Donkey in the Japanese dub of Shrek and in the first film of the series, one of both Shrek and Donkey's first villains they faced was Lord Farqaad, who was voiced in Japanese by Masato Ibu, who voiced the original Dessler.
To hammer it in even further, Yamadera played Kodai in the 2009 film Space Battleship Yamato: Resurrection. Ibu also had a role in there as Captain Gorui.
In a similar way, Daisuke Ono (Susumu Kodai) voiced Dwayne Hoover in the Japanese dub of Little Miss Sunshine, whose biggest dream is becoming an Air Force pilot and failing to do so. Kodai, on the other hand, not only is a member of the army, he also flies too as well.
Melda and Akira, also overlapping with Foe Yay in the beginning before Melda becomes an emmisary for Garmilas onboard the Yamato.
Moral Event Horizon: The beginning of episode 15 shows the Gamilan Imperial Guard dealing with a rebellion on one of the Empire's worlds by destroying every population center on the planet's surface, with multiple shots of the terrified inhabitants holding their loved ones close just before they're obliterated. And to top it off, the guy in charge of it all acts like the unfolding genocide is something they ought to enjoy.
Shocking Swerve: Dessler in episode 23, in a fashion very similar to Schniezel. While prior episodes had depicted him as an enigmatic, yet conciliatory ruler who had created the process of integrating conquered Gamillas species into the empire instead of just massacring or enslaving them, he is willing in episode 23 to wipe out his capital city filled with loyal members of his staff and devoted followers just so he can cement Iscandar's unification with Gamilas. With the power and influence he had, Dessler could have simply ordered it to be that the capital city be moved, and many would've listened, making his penultimate plan purely For the Evulz.
Tear Jerker: The death scenes of major characters, and related events:
Commander Shultz's final moments before his ship is destroyed while pursuing the Yamato and getting too close to a star - he recalls his wife and daughter whom he will eventually leave behind upon his death, considering earlier, and in a previous episode, he was watching a hologram message from his daughter greeting him and telling him to come home after his tour of duty is done.
Yuki's apparent death, which leaves Kodai hearbroken for most of the final episode, though he does his best to keep it hidden, until his Anguished Declaration of Love. He and Yuki eventually get better after Mamoru's intervention.
Okita's death, not long after. He takes a final last look at the Earth from his sickbed in his cabin, tearfully looks at a picture of his family, then quietly passes on.